Localised surface plasmon resonance inducing cooperative Jahn–Teller effect for crystal phase-change in a nanocrystal

The Jahn–Teller effect, a phase transition phenomenon involving the spontaneous breakdown of symmetry in molecules and crystals, causes important physical and chemical changes that affect various fields of science. In this study, we discovered that localised surface plasmon resonance (LSPR) induced the cooperative Jahn–Teller effect in covellite CuS nanocrystals (NCs), causing metastable displacive ion movements. Electron diffraction measurements under photo illumination, ultrafast time-resolved electron diffraction analyses, and theoretical calculations of semiconductive plasmonic CuS NCs showed that metastable displacive ion movements due to the LSPR-induced cooperative Jahn–Teller effect delayed the relaxation of LSPR in the microsecond region. Furthermore, the displacive ion movements caused photo-switching of the conductivity in CuS NC films at room temperature (22 °C), such as in transparent variable resistance infrared sensors. This study pushes the limits of plasmonics from tentative control of collective oscillation to metastable crystal structure manipulation.

visible-near-infrared (UV-Vis-NIR) absorption spectra were recorded using a UV-3600 spectrophotometer (Shimadzu). The temperature-dependent resistivity was measured using the van der Pauw method and a ResiTest8400 (TOYO Corporation) equipped with a cryostat.

Sample preparation and TEM observations
A suspension containing CuS and ethanol was dropped onto a carbon-mesh grid to fabricate the TEM sample. TEM images and diffraction patterns were acquired using Cs-corrected TEM with a cold fieldemission gun (JEOL JEM-ARM200F) and an accelerated voltage of 200 keV. A light-irradiation TEM specimen holder was used for observations with and without light irradiation. The specimen holder loaded the specimen into the microscope column containing a thin SiO2 rod and mirror in its head, an optical fibre connected the 170-mW Xe lamp (PE300BF, Cermax). UV-Vis light could reach the specimen through the rod reflected by the mirror. S1 Since the efficiency of reflection of the mirror is approximately 80%, the power of light irradiated on the sample was approximately 140 mW/cm 2 .

Simulation procedure
Diffraction patterns were calculated using the abtem S2 library of Python. The thickness of the sample was set to 50 Å during calculations, and the incident beam direction was [0001]. The STEM mode with a small convergence angle was used, and only the Cu atoms were assumed to exhibit movement (by 1 Å [fixed] in eight directions) due to light irradiation.

TEM results and deformation by light irradiation
The TEM images are shown in Figure S2. The images are slightly blurry (with a visible lattice fringe) because of the vibration of the sample holder connected to the optical fibre. The diffraction patterns from this particle are shown in Figure S3. To confirm atomic transfer under light irradiation, the intensity difference of the diffraction patterns between the light-on-light-off conditions were calculated. Similar calculations were carried out for the simulated diffraction patterns, and the results were compared. The best-matched results and their atomic arrangements are shown in Figure S3. They did not match the difference results exactly; however, the diffraction pattern differences between the light-off and light-on conditions could be attributed to the movement of Cu atoms.

Cu T displacement and diffraction pattern intensity
The differential patterns between the diffraction pattern of the original CuT position (light-off in the case of the experiment) and that of CuT displacement (light-on in case of the experiment) were compared to search for the best candidate for CuT displacement in the experiment. The diffraction patterns depending on CuT positions were simulated using ReciPro, a comprehensive crystal analysis software. S3 The diffraction pattern simulations were carried out for sixteen cases in which CuT atoms were set at a constant distance from the original position and with a π/8 step from the a-axis. The 1 3 0 and 2 3 0 spots were mentioned in the main text, and the 1 1 0 and its equivalent spots, indicated with black arrowheads in the right column of Figure S4, were observed for comparison. It was found that the displacement of CuT caused the focused spots intensity to change, but the optimum CuT displacement could not be determined from the difference. From the results, one example of the atomic arrangement and diffraction patterns is shown in Figure S4.  The c-axis lies vertical to the plane of the paper, and the atomic movement has been magnified in these figures for easier understanding. The middle and lower rows show the simulated and experimental results, respectively. The left and middle columns show the light-on and -off conditions, respectively, while the right column shows their differences. In the differences, black arrowheads have been added as highlights to indicate spots where the experimental and simulation results vary. Figure S5. Full width at half maximum (FWHM) of diffraction spots with and without light illumination.

Estimation of temperature increase by laser heating
To clarify the photo-thermal effect on the CuS NCs by the 400-and 800-nm light, we estimated the temperature rise caused by the incident light. Using the fluence of incident light ( , 5 mJ cm -2 ), absorptivity ( ), film thickness ( , 60 nm), specific heat ( , 0.5 J K -1 g -1 ) 1 , and density ( , 4.64 g cm -3 ) of CuS NCs, the temperature rise ( ) induced by the 400-and 800-nm light were calculated to be 30 and 11 K, respectively using the following equation: where the absorptivity is 3.2% for 800 nm and 8.5% for 400 nm, as shown in Figure S6. The diffraction intensity change due to temperature rise can be estimated using the Debye-Waller factor of the diffraction intensity; however, the Debye-Waller B-factors of CuS in the covellite structure have not been reported. Therefore, we estimated the diffraction intensity change due to temperature rise using the mean square displacement of the atoms from the linear compressibility and atomic distance of CuS. Because the atoms in a crystal randomly vibrate with a force constant ( ), the mean square displacement ( ) of atoms is expressed as follows S4 Δ 2 where, is the Boltzmann constant. The force constant can be derived from the linear compressibility ( , 3.77×10 12 1/Pa) S5 and atomic distance ( , 2.19 Å) as The Debye-Waller B-factor ( ) and Debye-Waller factor of the 1 1 0 diffraction intensity ( ) were calculated from the mean square displacement as 8 exp • where is the scattering vector from the (110) plane. In the kinematic theory of diffraction, the diffraction intensity ( ) is proportional to the square of the Debye-Waller factor as ∝ | | .
Thus, it was confirmed that simple photo-thermal effects did not cause photoinduced changes in the diffraction pattern of CuS NCs.
The Debye-Waller analyses were based on bulk CuS, and the experimentally obtained values for the Debye-Waller effect ( Figure S7) are more appropriate for estimating the rise in temperature of CuS NCs by photoexcitation. According to the fitting curve in Figure S7c, the intensity changes due to temperature rises of 11 and 30 ºC, corresponding to 0.44% and 1.2%, respectively, are still negligible.      increasing temperature, the CuS film exhibited semiconductive behaviour. It confirmed that the rise in temperature caused by IR irradiation did not decrease conductivity.